Massachusetts Senate leaders unveiled a $41.4 billion budget on Thursday that plows taxpayer dollars into health care for people who are poor and people with disabilities, K-12 education, and aid to cities and towns — without proposing any new broad-based taxes.

Though the budget relies on new revenue coming in from marijuana sales, taxes on short-term rental properties, and resort casinos, top officials in the liberal-leaning chamber did not include any big new taxes.

“Budgets are statements of priorities, and this budget is a clear declaration of support for children and families, statewide transportation, health care, education, and our most vulnerable populations,” said Senate President Harriette L. Chandler, a Worcester Democrat.

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On several important fronts, the Senate budget mirrors the House spending plan, passed last month, and Governor Charlie Baker’s budget, which was unveiled in January. The current budget for fiscal year 2018 is $40.2 billion.

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“This year, the similarities among the proposals outnumber the differences, which could be due in part to the small amount of discretionary dollars available,” said Eileen McAnneny, president of the business-backed Massachusetts Taxpayers Foundation.

All three put the single largest chunk of money toward MassHealth, the state’s Medicaid program for people who are poor or disabled, and other health and human services efforts. (Those areas usually make up about half of state spending each year.)

All three funnel more money into aid for cities and towns and K-12 education.

All three come up with a little bit more money to pay for social workers at the long-troubled Department of Children and Families.

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All three would offer a modest increase to the University of Massachusetts system, about 1 percent.

All three would make a relatively small investment in the state’s emergency rainy day fund, socking away $96 million.

And all three would raise the Earned Income Tax Credit, which helps the working poor.

It is “a tax credit that really helps low-income working families to be able to make ends meet,” said Noah Berger, president of the left-leaning Massachusetts Budget and Policy Center. “There’s a lot of evidence that when you raise the incomes of those low-wage working families, it has long-term positive effects on their kids: They do better in school; there are better health outcomes.”

But there are some differences as well.

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Like the House, the Senate is rejecting Baker’s effort to move 140,000 low-income adults off Medicaid and onto private plans to save the state money.

The Senate devoted $88 million to regional transit authorities, giving the 15 local agencies the funding they’ve called for and a roughly $8 million boost over what Baker and the House proposed.

And Senate leaders did not include any initial proposals aimed at the State Police, which have been beset by a series of scandals and revelations of hefty overtime payments in recent months.

But Senator Michael O. Moore, a Millbury Democrat and Senate chairman of the Legislature’s public safety committee, said a group of senators is considering amendments that could “work with and expand upon” changes the House included in its own spending plan to expand oversight of the police agency.

House leaders proposed creating a “special audit unit” within the State Police that would operate independently of the department and under the direction of the inspector general’s office. They also want to assemble a special legislative commission to study promotion policies at the State Police, in addition to tasking the Collins Center for Public Management at the University of Massachusetts Boston with making recommendations about how to improve the agency’s “overall management structure.”

Reports for each would be due at the end of the year under the House proposal.

“We’ll go along with the concepts. How we get there may be different,” Moore said. “We’re discussing different options.”

Senators must submit budget amendments by Monday. The chamber will begin debate on May 22. After it passes its final version, the House and Senate will hash out their differences.

The final state budget is expected to be signed by the governor around July 1, when the new fiscal year begins.

But the months-long Beacon Hill budget process comes amidst significant uncertainty over how taxes in Massachusetts will look next year. Two separate ballot questions — one raising income taxes on the very wealthy and one lowering the sales tax for everyone — may be put to voters in November, which could substantially scramble the state’s revenue picture.

And then there’s also national economic volatility, from a potential trade war with China to wild swings in the stock market.

Senator Karen E. Spilka, chairwoman of the Senate budget-writing committee, indicated she is cognizant, too, that the country’s economy has been in a recovery for nine years and that, if history is any guide, economic upswings don’t last forever.

“It’s not a matter of if there’s going to be a recession,” she told reporters at the State House Thursday. “It’s a matter of when.”